Introduction

A cross section is a profile showing geological features in a vertical plane through the earth. Some geologists prefer the term "section" for this type of diagram, reserving "cross section" to denote a section made perpendicular to structural strike. In practice, relatively few of these diagrams can be constructed strictly perpendicular to strike. Also, the word "section" used alone could be misconstrued to mean seismic Section, columnar section, or even thin section. in petrology, a section is a lithologic sequence which can be viewed in outcrop. In paleontology, a section is an important division of a genus. On public lands, a section is a smaller division of a township. To avoid ambiguity, many geologists have come to use the term "cross section" to describe a geological profile made across the earth, i.e., along any vertical plane through the earth, regardless of its orientation to structural strike. The term "dip section" is used to indicate cross sections made perpendicular to strike. we have adopted this more general definition of "cross section" since we believe that any practical study guide should reflect the most common and current usage of terms.

There are two categories of cross sections: structural and stratigraphic. Structural cross sections illustrate present-day structural features such as dips, folds, and faults. Stratigraphic cross sections show characteristics such as formation thicknesses, lithologic sequences, stratigraphic correlations, facies changes, unconformities, fossil zones, and ages. Simplification of structural elements permits greater emphasis on stratigraphic relationships in a stratigraphic cross section.

Since cross sections are drawn to scale, the locations of features on the diagram are measured off with respect to an arbitrary horizontal reference line called a datum. Structural and stratigraphic cross sections differ fundamentally in the type of datum line used. Structural cross sections are scaled off from a datum which represents an elevation; stratigraphic cross sections are based on a datum which represents a flattened stratigraphic boundary.

Cross sections are useful in the search for potential hydrocarbon traps which exist at depth in the earth. The petroleum explorationist uses cross sections both as working diagrams for problem-solving and as finished illustrations for display. As working diagrams, cross sections are helpful in the visualization of regional and local geological relationships. Simplification to two dimensions often facilitates interpretation, especially in geologically complex areas. Interpretive problems are frequently resolved during the working and reworking of one or more cross sections.

Cross sections are also useful for display purposes. Diagrammatic cross sections show broad relationships and serve to orient the audience to the general geology of a region ( Figure 1 ).

Figure 1

More detailed cross sections usually cover a smaller area and are invaluable in communicating the geologist's interpretation of a prospect. Such cross sections complement geological maps and geophysical data in an integrated exploration program.

The Elements of a Cross Section The geologist must answer a number of fundamental questions and must make a number of important decisions before a cross section is constructed. What will the cross section illustrate? Will it be a structural or a stratigraphic cross section? Will it be used to communicate broad relationships or to illustrate great detail? Is it for problem-solving or for display? What are the geological features of interest? What data will be used? How should the scale be chosen? Each decision should be made with the ultimate purpose of the diagram in mind. Such planning is the key to an effective cross section.

Input Data

Different types of data can be used in developing a cross section. The diagram may be based on outcrop information, or on subsurface data derived from wells and geophysical surveys, or it may use both outcrop and subsurface data.

Cross sections which use outcrop information are particularly useful in frontier areas of petroleum exploration, where subsurface information is often sparse or unavailable. In covered areas between outcrops, the geologist can infer information from soil type,

vegetation, and topography. Shallow data control is therefore fairly continuous wherever surface geology is used.

Many geological cross sections made for petroleum exploration rely on subsurface data. The information for such cross sections comes primarily from wells, and thus the data is not continuous over the length of the cross section. Supplemental geophysical data can be helpful in interpreting between the data points. It is generally desirable to have data points relatively evenly spaced along the line of section, wherever this is permitted by well control. However, a greater density of information may be necessary over a feature of special interest. For instance, additional data points are often chosen over a fold or on each side of a known or suspected fault. The reliability of data is another important factor which must be considered. All data should be checked for accuracy. Incorrect well location or elevation information is a common source of error, especially in old wells. This information is easily verified in areas of relief by plotting the wells on topographic maps to determine if the given elevation is reasonable.

Incorrect stratigraphic tops are another possible source of error. Drillers' picks are particularly prone to mistakes and should be compared with adjacent wells. Wherever possible, log tops should be used in place of drillers' picks. The geologist should recorrelate all logs to ensure accuracy and consistency. A third source of error is borehole deviation, i.e., when the well is not drilled vertically, but at some angle to the vertical ( Figure 1 ,

Figure 1

Distortion of true thickness (t) and true dip () measurements due to borehole deviation; tA= apparent thickness and A= apparent dip.) Depth and dip measurements assume that the hole was vertical and are therefore distorted by borehole deviation. The distortion can be corrected only if a downhole directional survey exists. Deviation in recent wells is usually intentional and directional surveys are usually available. If such a survey exists, true depth and dip can be calculated and incorporated into the cross section. If the deviated well happens to lie in or near the plane of section, the actual trace of the hole can be drawn on the section with the help of the directional survey. If the borehole does not lie in the plane of section, or if it is deviated in three dimensions, it must be projected onto the cross section. This projection of the borehole will show apparent, rather than actual deviation ( Figure 2 , Cross-sectional projection of a borehole deviated in three dimensions.

Figure 2

Segments of the borehole which do not lie in the plane of section are dashed onto the cross secions. Due to foreshortening, the dashed segments show only apparent deviation. This can be seen by comparison with the inset plan view). One should always be cautious in accepting the conclusions of previous studies. Many authors from the academic community who write "definitive" papers have access to less data than do petroleum industry personnel. This is not to say that industry-generated studies should be blindly preferred to academic studies. The geologist should screen every potential resource carefully. The expertise of authors should be assessed; the extent and reliability of their data should be checked; and the validity of their conclusions should be scrutinized. Occasionally, it is useful to verify maps and cross sections with small sketches. Seismic interpretations should be reviewed,

usually with the help of a geophysicist. Even in-house studies should be subject to this examination. Careful control over the quality of data input is essential to the construction of an accurate cross section.

Line of Section

After gathering available data, the next in cross section development step is to choose the line of section, i.e., the line along which the cross section would intersect the surface of the earth ( Figure   1 ).

Figure 1

The approximate location of the line of section is largely determined by the location of the features of interest. The orientation of the line is primarily controlled by the nature of the geological relationships to be illustrated and by the availability of reliable data.

Cross sections may trend perpendicular to strike, oblique to strike, or parallel to strike ( Figure   2 ).

Figure 2

These cross sections are termed dip sections, oblique sections, and strike sections, respectively. one must bear in mind that the dip shown on an oblique or strike section is always less than true dip. The greater the angle between the true dip direction and the line of section (), the greater the difference between the true dip () and apparent dip (A). Mathematically, the relationship between these variables is expressed as:

tanA = tan cos     (1)

Minor manipulation of Equation 1 will demonstrate that apparent dip may vary between horizontal, where the line of section is parallel to strike (= 70), and true dip (), where the line of section is perpendicular to strike (= 0) ( Figure   3 ,

Figure 3

Vertical profiles of the top of the jenny sand, made along the lines of section illustrated in Figure   2 . True dip is shown by profile XA which trends perpendicular to structural strike). Thus, quantitative dip measurements will be distorted in cross sections which are not made perpendicular to strike.

Since it is unusual to find a succession of wells along a straight line, many cross sections which use well data follow zig-zag paths. Lines of section may change direction or even trend in a circle if necessary to illustrate the desired geological features ( Figure   4 , Line of section across a field in Wyoming. The circular path was necessary in order to illustrate the nature of the stratigraphic hydrocarbon trap).

Figure 4

The apparent dip of horizons on a cross section will vary from segment to segment as the orientation of the line of section changes. Thus, an irregular line of section will affect the shape of the geological features illustrated in a cross section ( Figure   5 and Figure   6 ,

Figure 5

Two structural cross sections through the same geological feature).

Figure 6

It is desirable to choose as straight a line of section as possible.

Some geologists project nearby wells into a straight line of section instead of deflecting the line of section to the wells. It is usually necessary to construct a subsurface contour map before projecting wells.

The location of the well on the cross section is determined by a normal from the well to the line of section, or by projecting the well along strike. The well is dashed onto the cross section to distinguish it from any wells which actually lie in the plane of section ( Figure   7 ).

Figure 7

A correction is made for any change in the apparent dip of beds, using Equation 1. This procedure is useful for diagrammatic structural cross sections, or when projected wells are close to the straight line of section. In other circumstances, it is best to take the line of section right up to the well.

Geology sometimes makes a zigzag line of section undesirable. If the required well is too far away to project onto the section, information from the well still may be used in interpretation. In such a case, a small cross section to the unillustrated well may be inset above the point to which the well would have been projected. This inset clarifies the geologist's interpretative reasoning.

Scale

After the line of section and data points have been chosen, the geologist must decide on the scale of the cross section. There are actually two scales to consider: one horizontal and one vertical. For convenience in construction and cross reference, the horizontal scale is often taken to be equal to the scale of corresponding geological maps. The vertical scale may or may not be equal to the horizontal scale, depending on what the cross section is intended to illustrate.

Greater stratigraphic detail can be shown if the vertical scale is large. However, if the horizontal scale were to be made equally large, the cross section might become absurdly

long. In such cases, the horizontal scale is taken to be smaller than the vertical scale, a technique called vertical exaggeration.

When using vertical exaggeration, the vertical scale is usually chosen to be some easy multiple of the horizontal scale. The degree of exaggeration in the vertical direction, V, can be expressed as:

V = Iv/Ih       (1)where Iv and Ih are the lengths of a unit distance on the vertical and horizontal scales, respectively.

In petroleum exploration, some vertical exaggeration is usually employed in order to show sub-Surface features in sufficient detail. However, distortion is introduced when the horizontal and vertical scales are different.

Dips in an exaggerated cross section show a nonlinear deviation from true dip. The relationship between true dip, , and exaggerated dip, E, is expressed as:

tan E = V tan        (2)where V is vertical exaggeration as defined by Equation 1. True dip occurs where V = 1.

The difference between two very gentle true dips is accentuated by vertical exaggeration, while the difference between two steep true dips is diminished. Vertical exaggeration, therefore, highlights relationships between features which are nearly flat-lying, while it makes it more difficult to distinguish between features with steeper dips. For instance, on a cross section with a vertical exaggeration of 8, beds dipping 3o E and an unconformity with a dip of 6o E will have apparent dips of 23o and 40o, respectively. On the same cross section, a thrust fault with true dip of 39o W and a normal fault with true dip of 63W will show respective apparent dips of 81o and 86o ( Figure 1 and Figure 2 ).

Figure 2

Figure 1

Formation thicknesses are also distorted by vertical exaggeration ( Figure 3 ).

Figure 3

In an exaggerated cross section, the vertical component of all distances is multiplied by the factor V as defined in equation 1. When defined in this manner, the factor V does not affect the horizontal component of distances on the cross section. Thus, in Figure 3 , distances measured horizontally remain the same in both the exaggerated (b) and unexaggerated (a) views, while distances measured vertically are multiplied by a factor of V = 2 in the exaggerated view. The exaggerated thickness of strata tE, will vary as the exaggerated dip of beds changes from horizontal to vertical. When the beds are vertical, thickness is measured horizontally and tE = t, where t is true thickness. When the beds are horizontal, thickness is measured vertically and tE = Vt. Thus, in a vertically exaggerated cross section where V>1, a bed will appear thickest in areas of gentle dip and will thin as dip increases. This results in an apparent attenuation, or thinning of strata in areas of steepening dip, for instance on the flanks of a fold ( Figure 3 ).

Of course, vertical exaggeration involves two variables: the vertical and horizontal scales. We could look on the distortion as a shortening in the horizontal direction, in which case the horizontal component of all distances would be modified by a factor of 1/V. This is merely another way of looking at the same relationship. Whichever point of view you may wish to adopt, the salient point to remember is that vertical exaggeration results in an apparent attenuation or thinning of strata over areas of steeper dip. Quantitative features such as dip and formation thickness are preserved where the horizontal and vertical scales are equal. Although these features are distorted when the scales are not equal, important geological relationships can be emphasized. Used wisely, vertical exaggeration is an effective tool in the construction of cross sections. The decision to employ vertical exaggeration is based on what the cross section is intended to illustrate and on how one can most effectively achieve

that illustration. An exaggerated cross section should be clearly labeled with bar scales and the value of v. For quick reference, it may also be helpful to include a small inset with an unexaggerated view of the cross section ( Figure 2 ).

Practical considerations also affect the choice of scale. The most important factor is that the overall size must be adequate to show the desired detail. In addition, the cross section should be large enough to be visible from a distance if it is intended for display. However, one must take care that the figure will fit available reproducing machines. Overly large cross

seDatum

The chosen vertical scale will be used to measure off tops and bases of geological boundaries on the cross section. However, the measurements must be made with respect to some reference line. The line is a one-dimensional representation of a feature or surface which is continuous over the area covered by the cross -section. Regard less of the actual relief of the feature or surface, it will be represented by a straight horizontal line, and it will be used as a reference when scaling off boundaries on the cross section. Such a reference line is called a datum line, and the feature or surface represented by the datum line is called a datum plane.

An elevation is one common type of datum plane ( Figure 1 , Sea level was used as a datum for this cross section).

Figure 1

Geological boundaries may be scaled off from the corresponding datum line according to their known elevations in each well. Since elevation planes are already horizontal, existing spatial relationships are preserved and the resulting cross section shows present-day geological structure. Cross sections using an elevation datum are called structural cross sections.

The other type of datum plane is a stratigraphic boundary ( Figure 2 ). The boundary may be on a marker horizon or on an unconformity. The most important criteria for choosing a stratigraphic datum are that the boundary be easily recognized and reasonably widespread.

Figure 2

Few stratigraphic boundaries are horizontal, yet a stratigraphic datum plane is shown as a straight horizontal line on the cross section. For this reason, it is known as a flattened stratigraphic datum. Cross sections which are based on this type of datum are called stratigraphic cross sections. Since the reference boundary is not an elevation, it is no longer possible to simply scale off elevations relative to sea level. Instead, the interval from the datum boundary to the desired horizon is scaled off in each well.

Flattening a stratigraphic boundary causes changes in the geometrical relationships of geological features (compare Figure 1 and Figure 2 ). The resulting cross section illustrates

paleostructure, i.e., structural relationships which existed at the time of deposition or formation of the stratigraphic datum horizon. If a cross section is intended for paleostructural analysis, then it is important to choose a datum of appropriate age for the desired results. Whenever available, a timestratigraphic unit such as a bentonite or a lava flow should be used. Care should also be taken to ensure that the chosen datum horizon does not reflect paleotopography.

ctions are unwieldy as well as being expensive or even impossible to reproduce.

What type of cross section would you construct if:

(a) You were interested in the relationship of subsurface features 1 million years ago, and;

(b) you wanted to see how these features changed over a large region, and;

(c) the features are thin and have a very gentle dip?

The fact that you are interested in paleostructural relationships rather than current ones dictates the choice of a stratigraphic section. These sections are not tied to present-day topography or to a fixed elevation, but to a particular stratigraphic horizon. The horizon may be tilted, folded, faulted or eroded at the present time, but the stratigraphic section visualizes it as if it was flat. This makes it much easier to understand past geological conditions and can be helpful in locating areas where hydrocarbons might have formed or been trapped.

In this case, the fact that the features are not dramatic together with the vast horizontal scale of a regional section strongly indicates the use of vertical exaggeration. Without multiplying vertical distances the features of this section would be so thin that the section would show virtually nothing. By enlarging the vertical scale several times, beds can be enlarged, dip angles steepened, and trends accentuated. This creates distortion, but given the nature of the section this is justified by the benefits of greater structural clarity.

What type of cross section would you construct if:

(a) You wished to know if a present-day surface feature was reflected in a similar subsurface structure, and;

(b) the area you were interested in was fairly small, and;

(c) it was important that the section not distort the thickness of the strata it depicted?

The need to depict current structures-including topography-dictates the use of a structural cross section. This type of section is tied to actual elevation and represents as accurately as possible the folds, faults, and unconformities of an area. It is intended to reveal subsurface structures that might, for instance, form hydrocarbon traps. In our specific example it is used to verify the presence or absence of a surface feature at depth. If the feature is a dome or an anticline-and if it does exist at depth-then it might commend itself as a drilling prospect.

In this case, the structures of interest are not dwarfed by the area covered in the section, so vertical exaggeration is not necessary. By matching the vertical scale to the horizontal scale

actual spatial relationships can be preserved. Because it is important that the features of your section not be distorted, it is preferable not to use any vertical exaggeration.

What are common sources of error in cross sections and how are they avoided?

Constructing cross sections is an inferential process, and the results are largely speculative. Our perceptions of the subsurface are usually based on limited data which often lend themselves to more than one interpretation. Perfect accuracy is unlikely especially with complex structures, and minor errors are therefore inherent in the process. It is especially important, however, to avoid large errors which could detract unnecessarily from the accuracy of a section. Errors of this type usually fall into three categories:

(a) Faulty data-the gathering of all data is subject to error. Sources, especially older ones, should be screened on the basis of reliability. Common errors in older data include incorrect well locations and elevations. Hard data-like logs-are preferable to more subjective information like drillers picks.

(b) Faulty interpretation of data-the conclusions of previous geologists may be inaccurate. Misinterpretations can be perpetuated if prior work on an area is accepted without question.

(c) Insufficient data-wells may be spaced too widely to generate a reliable section. Structural details may be glossed over if supplementary data (seismic, etc.) is not available.

(a) Using the relationship

tanE = V tan ,

where E = exaggerated dip angle, V = vertical exaggeration and = true dip angle,

fill in the blanks in this table.

    

VERTICAL EXAGGERATION

TRUE DIP EXAGGERATED DIP

1a.  7 65 degrees ____1b. 7 80 degrees ____2a. 4 ____ 71 degrees 2b. 

  4 ____ 78 degrees

 3a. ____ 4 degrees 35 degrees 3b.  ____ 6 degrees 47 degrees  4a.  5 _____ 32 degrees 4b. 5 14 degrees ____

(b) What general rule can you observe in 1a and 1b?

(c) ... in 2a and 2b?

(d) What can you observe in 3a, 3b and 4a, 4b?

(a) Missing information in table: 1a. Exaggerated Dip = 86° 1b. Exaggerated Dip = 89° 2a. True Dip = 36° 2b. True Dip = 50° 3a vertical Exaggeration = 10 3b. Vertical Exaggeration = 10 4a. True Dip = 7° 4b. Exaggerated Dip = 51°  

(b) Vertical exaggeration tends to decrease the angular difference between two steeply dipping surfaces. The difference in True Dip between 1a and 1b is 15 degrees, while the difference in Exaggerated Dip is only 3 degrees.

(c) The same effect is evident in this example, too. However, because the vertical exaggeration is much less and the true dips are not quite so steep the effect is less pronounced. In 1a and 1b the difference between the true dips is five times as great as the difference between the exaggerated dips. However, in 2a and 2b the difference between the true dips is only two times the difference between the exaggerated dips.

(d) The effect of vertical exaggeration is just the opposite on gently angled strata. Minor differences at low dip angles are greatly increased in cross sections that are vertically exaggerated. A 2-degree difference in true dip in 3a, 3b is magnified to a 12-degree difference in exaggerated dip; and a 7-degree difference in 4a, 4b magnifies into a 19-degree difference. Vertical exaggeration is therefore more useful in distinguishing between slightly dipping structures than between sharply dipping structures.

Structural Cross Sections

In petroleum geology, most structural cross sections are begun by drawing a horizontal datum line which represents an elevation. Wells may be represented by lines drawn to scale, called sticks, or by well logs reduced to the appropriate vertical scale. In both cases, the horizontal distance between adjacent wells is measured off on the horizontal scale, and the wells are hung on the datum by matching up the datum line with the corresponding elevation in the well. When sticks are used, it is necessary to scale off the elevations of formation boundaries from the datum. If well logs are used, it is only necessary to mark correlative stratigraphic units in each log. Dipmeter readings and migrated seismic depths may also be plotted if they are available.

Whenever wireline logs are used, only two of the log curves are usually reproduced: one on the right side and one on the left side of the log print-out. The most commonly used curves are the self-potential or the gamma ray curves on the left and one density or resistivity curve on the right ( Figure 1 ). Other combinations are possible, depending on what logs are available and on what the cross section is intended to show.

Figure 1

Some structural cross sections extend up to the surface of the earth. Such cross sections are often topped by a topographic profile. This profile is derived from a geological outcrop map which shows topography (e.g., most geological quadrangle maps). The generation of the cross section is facilitated by taking the horizontal scale of the diagram to be the same as the scale of the map. The locations of topographic contours and geological contacts can then be transferred directly onto the cross section from the map.

In plotting a cross section by hand, we first draw the line of section on the map. Next, we place the base of the drawing paper along the line of section so that the westernmost end of the cross section will be on the left side of the paper. Mark off the points where the paper crosses contour lines, and use the chosen vertical scale to plot the corresponding elevations above each mark ( Figure 2 ). Connecting the elevation points gives rise to a completed topographic profile.

Figure 2

Next, we plot outcrop data on the topographic profile. We place the base of the drawing paper along the line of section and mark the points where the paper crosses geological contacts, faults, or dip measurements. This information is transferred vertically onto the topographic profile. We can check the accuracy of the plotted positions by comparison with the geological map.

When we draw in the dips ( Figure 3 ), it is important to remember that dip measurements must be adjusted if the cross section is vertically exaggerated.

Figure 3

This is done by solving E in the equation tanE = V tan.

Structural Cross Sections

In petroleum geology, most structural cross sections are begun by drawing a horizontal datum line which represents an elevation. Wells may be represented by lines drawn to scale, called sticks, or by well logs reduced to the appropriate vertical scale. In both cases, the horizontal distance between adjacent wells is measured off on the horizontal scale, and the wells are hung on the datum by matching up the datum line with the corresponding elevation in the well. When sticks are used, it is necessary to scale off the elevations of formation boundaries from the datum. If well logs are used, it is only necessary to mark correlative stratigraphic units in each log. Dipmeter readings and migrated seismic depths may also be plotted if they are available.

Whenever wireline logs are used, only two of the log curves are usually reproduced: one on the right side and one on the left side of the log print-out. The most commonly used curves are the self-potential or the gamma ray curves on the left and one density or resistivity curve on the right ( Figure 1 ). Other combinations are possible, depending on what logs are available and on what the cross section is intended to show.

Figure 1

Some structural cross sections extend up to the surface of the earth. Such cross sections are often topped by a topographic profile. This profile is derived from a geological outcrop map which shows topography (e.g., most geological quadrangle maps). The generation of the cross section is facilitated by taking the horizontal scale of the diagram to be the same as the scale of the map. The locations of topographic contours and geological contacts can then be transferred directly onto the cross section from the map.

In plotting a cross section by hand, we first draw the line of section on the map. Next, we place the base of the drawing paper along the line of section so that the westernmost end of the cross section will be on the left side of the paper. Mark off the points where the paper crosses contour lines, and use the chosen vertical scale to plot the corresponding elevations above each mark ( Figure 2 ). Connecting the elevation points gives rise to a completed topographic profile.

Figure 2

Next, we plot outcrop data on the topographic profile. We place the base of the drawing paper along the line of section and mark the points where the paper crosses geological contacts, faults, or dip measurements. This information is transferred vertically onto the topographic profile. We can check the accuracy of the plotted positions by comparison with the geological map.

When we draw in the dips ( Figure 3 ), it is important to remember that dip measurements must be adjusted if the cross section is vertically exaggerated.

Figure 3

This is done by solving E in the equation tanE = V tan.

Correlation and Geological Interpretation

Correlating data points require the use of geological principles and common sense. one set of data may give rise to more than one acceptable interpretation. In choosing between interpretations, one must first ensure that each approach is reasonable. Scrutinize the data, assumptions, and conclusions. Then make your final choice based on your knowledge of local and regional geology.

Figure 1 shows two SP logs, one for Well A and one for Well B.

Figure 1

The sandstone shown in each log has been correlated as a discrete formation. In Well A, the sandstone is at a higher elevation and it is water-wet. In Well B, the sandstone is at a tower elevation and is also water-wet, but it contains an oil show. Given this data, there are several possible interpretations: an anticlinal closure between Well A and Well B ( Figure 2 )

Figure 2

; a closure on the upthrown flank of a fault located between the wells ( Figure 3

Figure 3

); a closure on the downthrown flank of a fault between the wells ( Figure 4 ); and finally,

Figure 4

a permeability barrier ( Figure 5 ). The known structural and stratigraphic grain of the area would be used as a guide in determining which of these interpretations is the most likely to be correct.

Figure 5

The accuracy of the interpretation can be checked by comparison with other nearby studies, such as cross sections, geological maps, and geophysical surveys. Specific geological conditions sometimes permit special methods of checking for accuracy. For instance, the concept of volumetric accuracy, based on the principle of conservation of mass, is often used for structural cross sections in areas where concentric folding and thrust faulting have predominated.

The concept of volumetric accuracy holds that, since cross-sectional bed length remains constant during concentric deformation, the accuracy of a cross section can be verified by comparing the lengths of several marker horizons. The lengths are measured between two appropriate reference lines. These reference lines are chosen so that they lie in planes where interbed slip has not occurred, such as the axial planes of folds. The lengths of different beds between these reference lines should be equal unless the cross section is cut by a discontinuity. Interpretation of the type of discontinuity will depend on the available data and on local geological trends. For greater detail, the reader should refer to C.D.A. Dahlstrom's article (1969) which describes the use of volumetric accuracy in constructing

cCompleting the Cross Section

The cross section is completed by drawing in the final interpretation, and by labeling important features. Conventional colors and symbols are often used to show the geological nature of the features. some conventions, such as those for sandstone, are more universal than others; the choice itself is less important than consistency once the choice is made. Some common symbols are shown in Figure 1 .

Figure 1

Sandstone is often yellow with a stippled pattern; shale is grey with rows of dashed lines; limestone is blue with an orthogonal brick pattern; dolomite is pink, or sometimes blue, with a rhombic brick pattern. Salt is often colored white or orange with rows of small crosses. In special cases where crystalline rocks are shown, they may be colored red. Intermediate lithologies are illustrated by combining the appropriate patterns and by using the color of the predominant lithologic end member.

Pore fluid composition can also be indicated with colors. Gas is shown as red, oil is green, and water is colored blue.

Clear labeling of all important features is essential to an effective cross section. Horizontal and vertical bar scales should also be clearly shown so that the scale is retained if the cross section is photographically reduced or enlarged. In addition, every cross section should include a title, the location and orientation of the line of section, the degree of vertical exaggeration (V); and the author, date, and data sources.

ross sections through the Alberta foothills region of Canada.

Once you have decided what type of cross section you need, what is the construction procedure?

Based on what you want to know, you will choose a line of section that best reveals the features you are interested in. If you are constructing a structural cross section which includes surface topography, you will now add information from a contour map. By matching the scale of the section to that of the map it is possible to transfer elevations directly from one to the other. Elevation points are then connected to form a topographic profile. using the same procedure geological information can be transferred.

Next, a horizontal datum line is established. It will extend across the diagram and all depth data will be keyed to it. With structural cross sections the datum line is an elevation; with stratigraphic cross sections it is a prominent stratum or other noteworthy plane. Such a plane must be uninterrupted over the full area depicted in the section, and it must not reflect any features of paleotopography. Moreover, the choice must be appropriate for the purpose of each individual cross section.

Data, usually in the form of logs or stick wells, are now sequenced and "hung" on the datum line. The logs or stick wells are scaled off at distances corresponding to actual well spacing. Once each column of data has been keyed to the horizontal datum, initial correlation can begin. As identical horizons in each chart are connected, discontinuities may emerge. The resolution of these questions will take place during the final stages of interpretation.

Once the hard data has been organized and positioned it is a good practice to ink it in before starting the final stage of interpretation. with that done, it is possible to rework the section many times without disturbing the basic data. Specific instructions for the interpretation phase are difficult to give. Each situation is different. Experience and intuition play a big role in filling in the geology between wells.

Information is given below for four wells and one columnar section in northwestern Montana. use the information to construct a stratigraphic cross section on top of the Mississippian. You will need to know that the evaporitic Potlatch Formation is the eastern facies equivalent of the Wabamun Dolomite. All distance measurements are given in feet. ( Figure 1

Figure 1

)

DISTANCES BETWEEN DATA POINTS

Outcrop to Well A: 26500 ft E

Well A to Well B: 21000 ft E

Well B to Well C: 10500 ft E

Well C to Well D: 10500 ft E

Well A

ELEVATION: 4291 (DF)

TOTAL DEPTH: 6642

LOG PICKS:

Mississippian (unconformity)              4622

Sun River                                                 4622-4780

Lodgepole/Mission Canyon                 4780-5850

Devonian (unconformity)                      5850

Potlatch                                                     5850-6070

Nisku                                                         6070-6090

Duperow                                                   6090-

REMARKS: D&A

Well B

ELEVATION: 4347 (DF)

TOTAL DEPTH: 4692

LOG PICKS:

Mississippian (unconformity)                 2872

Sun River                                                    2872-3023

Lodgepole/Mission Canyon                    3023-4050

Devonian (unconformity)                         4050

Three Forks                                                 4050-4075

Potlatch                                                       4075-4295

Nisku                                                            4295-4338

Duperow                                                      4338-

REMARKS: D&A

 

Well C

ELEVATION: 3750 (DF)

TOTAL DEPTH: 3450

LOG PICKS:

Mississippian (unconformity)                    1910

Sun River                                                       1910-1980

Lodgepole/Mission Canyon                       1980-3050

Devonian (unconformity)                            3050

Three Forks                                                    3050-3115

Potlatch                                                           3115-3290

Nisku                                                                3290-3350

Duperow                                                          3350-

REMARKS: 200 BOPD

Well D

ELEVATION: 3714 (DF))

TOTAL DEPTH: 3590

LOG PICKS:

Mississipian (unconformity)                          1950

Lodgepole/Mission Canyon                           1950-3070

Devonian (unconformity)                                3070

ELEVATION: 3070-3158

Potlatch                                                               3158-3298

Nisku                                                                   3298-3350

Duperow                                                             3350-

REMARKS: D&A

Figure   2

Information is given below for four wells. Use the information to construct a structural cross section. All

distance measurements are given in feet.

DISTANCES BETWEEN WELLS 

Unit 1A to Unit 2: 3850 ft SE 

Unit 2 to Unit 3:2250 ft SE 

Unit 3 to Unit 4:2400 ft SE 

Datum= -5000 ft.   Vertical exaggeration= 5 (500 ft. horizontal = 100 ft. vertical)  

Well-Unit 1A 

ELEVATION:  234 (KB) TOTAL DEPTH:  6154 DRILLERS PICKS: A Sand 5634-5724

B Sand  6102-6146

REMARKS: D&A  

Well-Unit 2  ELEVATION:  127 (KB) TOTAL DEPTH:  6127  

LOG PICKS:DIPMETER READINGS: 

A Sand  5317-5399  10 SE B Sand 5725-5770  15 SE

C Sand   Absent  ___

 REMARKS: Possible fault at 6067 ft

 Gas @ 5317-5377; 

5725-5757 ft

  Well-Unit 3

  ELEVATION:  252 (KB)

TOTAL DEPTH:  6212

LOG PICKS:DIPMETER READINGS:

A Sand  5617-5712 30 SE B Sand  Absent  C Sand  6075-6162 7 SE REMARKS:  Gas in C Sand;

G/W contact at 6102 ft

  Well-Unit 4

  ELEVATION:  398 (DF)

TOTAL DEPTH:  6400 

LOG PICKS:DIPMETER READINGS: 

A Sand 5518-5598 7 SEB Sand 5923-5961 7 SEC Sand 6281-6370 7 SE

REMARKS:Slight show of Gas at 5518 ft

 

                       

 

 

Figure   1

The Wyckoff Gas Field, located in Steuben County, N.Y., produces from Onondaga Limestone and/or Oriskany Sandstone. ( Figure 1 ) The Onondaga forms a thick biohermal reef over part of the field.

Figure 1

Only the porous core facies is productive in the reef section (see map). A deep-seated down-to-the-southwest fault extends upward along the southwest flank of the reef. Oriskany production is from a small

anticline on the upthrown side of the fault.

Elevations and marked logs are provided for 6 wells in the Wyckoff Field ( Figure 2 ,

Figure 2

Figure 3 , Figure 4

Figure 4

, Figure 5

Figure 5

, Figure 6

Figure 6

, and Figure 7 ).

Figure 3

Use this information to construct a northeast-southwest structural cross section from the Richards well to the Dibble well, showing the interval from top of Onondaga to bottom of Oriskany.

Figure 7

  Wyckoff Reef Gas Field  

WELL ELEVATION

CORNELL  2257' 

DIBBLE  2098' 

GUILD  2037'

CHASE  2206'

BANKS  2182' 

RICHARDS  2066' 

Figure 8

Figure   1

Fence Diagrams

In petroleum exploration, the development of a prospect is a three-dimensional problem. One of the drawbacks of cross sections is that they are limited to two dimensions. How can we illustrate the three-dimensional geology of an area?

The most common type of diagram showing geological relationships in three dimensions is a fence diagram ( Figure 1 ). Fence diagrams consist of a three-dimensional network of geological cross sections drawn in two dimensions. The diagram is built on a map base which is seen in plan view.

Figure 1

In constructing a fence diagram, the plane of the map base corresponds to the chosen datum plane, and the well location on the map is taken to be the point where the well intersects the datum plane. The wells are hung on the datum and then individual cross section panels are filled in, beginning at the front of the diagram.

In fence diagrams, one must consider the overall orientation of the figure, bearing in mind that panels oriented parallel to the viewing direction will appear only as straight lines. Such panels are usually omitted from the diagram. If important panels are not displayed to the best advantage, the viewing direction can be changed so that the features of interest are presented in the most effective way.

Front panels sometimes obscure parts of rear panels in fence diagrams. Where two panels overlap, the correlations on the front panel are drawn in with solid lines and highlighted with colors, while the correlations on the overlapped part of the rear panel are simply dashed in.

When the vertical scale is too large or the spacing of sections is too close, very large parts of the rear panels may be obscured ( Figure 2 ).

Figure 2

Usually, this problem can be minimized if the vertical scale and the panel spacing are carefully chosen. However, it is not always possible to change the scale or spacing without losing important details illustrated by the diagram. In such a case, one can construct an isometric projection of the fence diagram ( Figure 4 , only lines parallel to the North-South and East-West axes are undistorted).

Figure 4

The map base in an isometric projection is shown as if it was turned at an angle and tilted toward the viewer. The conversion is actually a transformation from orthogonal to nonorthogonal axes. A rectangular map base will become a parallelogram in an isometric projection ( Figure 3 and Figure 4 ).

Figure 3

All lines that were parallel to the original horizontal and vertical axes remain parallel to the corresponding new axes, and the scale along these lines also remains unchanged. However, lines which were not parallel to the original axes will be distorted. Points along such lines must be transferred onto

the projection by coordinates relative to the new axes. A grid sBlock Diagrams

Along with the fence diagram, another type of diagram illustrating three-dimensional geological relationships is a block diagram ( Figure 1 ).

Figure 1

This type of figure is a two-dimensional representation of a rectangular block. Two intersecting cross sections often form the sides of the block; the top of the block shows either a mapped surface or relief on the uppermost geological boundary shown in the cross sections. The block may be rotated to achieve the most effective viewing angle, and it may be drawn with or without the use of perspective.

Isometric block diagrams do not employ perspective. opposite sides of the block remain parallel, making the distant end of the diagram appear to be larger ( Figure 2 ,

Figure 2

Figure 3 , and Figure 4 ).

Figure 3

The top of this type of block diagram may be given any degree of tilt toward the viewer.

Figure 4

A large amount of tilt emphasizes features on the top surface of the block; a smaller degree of tilt brings out details on the sides of the block. Scales along the x, y, and z axes need not be equal.

The scale along the sides of the figure (y) is sometimes chosen to be smaller than the scale across the front and back edges (x), thus creating an illusion of perspective.

Perspective can be used in constructing block diagrams ( Figure 5 ).

Figure 5

In perspective blocks, all parallel lines with a component in the y direction converge to a vanishing point on the horizon. Sets of parallel lines with different orientations converge to different vanishing points. The cross section on the front face of the block is usually left undistorted by perspective. It is possible both to rotate the block about the z axis or to display it at different elevations relative to the horizon. Again, the choice of block orientation is made to emphasize the important features of the diagram.

ystem is helpful in this process.

Computer-Drawn Cross Sections

In some cases computers can facilitate the long process of cross section construction. A computer can generate cross sections rapidly and inexpensively. The information required is the same as for drafting a cross section by hand, however, the data must be translated into a code which the computer can read. Coded data and programs are convenient to store and to retrieve, permitting reproduction of old cross sections at any time. Perhaps most importantly, parameters are easily changed until the most effective diagram is obtained. Where needed, the computer programs themselves can always be revised or updated. Computer-generated cross sections are particularly useful as working diagrams used during the problem-solving stage.

It is important to be aware of the limitations of the computer. Parameters and limitations will vary depending on the type of computer and on the programs available for use. Properly instructed, the computer can incorporate the personal knowledge and experience of the geologist into the cross section it generates. However, computers do not make any interpretation beyond that made by the geologist when the data input was selected.

For instance, some cross section programs will not draw faults. In such cases, segments containing faults should be left blank by the computer and correlated by hand if the fault is desired on the cross section. Previously unknown fault locations may show up as distortions in the computer-drawn section. The geologist should examine the data surrounding such an anomaly and, if necessary, revise the cross section by hand.

There are several types of computer sections. In the simplest case, the computer can plot stick wells without showing correlation lines. The only input needed by the computer for this type of section is the specification of the scale, distances between wells, elevation of the wellhead, total depth, and the elevation of the datum in each well. If the wells are to be represented by logs, then the computer requires the logs in an acceptable digitized form. When connection of geological boundaries is desired, the boundary elevations in each well must also be specified.

Using the same method, many computers can draw fence diagrams from any viewing angle. The desired angle must be given, in addition to all well information and datum and geological boundary elevations.

Since fence diagrams are somewhat time-consuming to construct, the advantages of computer application are evident. Using the computer, it is easy to experiment with different parameters until the most effective diagram is obtained.

Gridded profiles are a second category of computer-generated cross section. Each subsurface geological boundary is treated independently in the gridded profile approach. First, the computer locates all data points which give the elevation of the boundary over the region in question. Next, the computer fits a grid over the available regional data. The geometric characteristics of the grid vary from program to program, depending on the desired time and storage efficiency. Common grid types are square ( Figure 1 ) or triangular. The size of the grid cell is an important variable.

Figure 1

Too large a grid spacing will cause smoothing which may eliminate significant details. When the grid is too small, large clusters of empty grid squares will occur between data points, which may result in inaccurate calculations for grid point values near the centers of the empty clusters. The optimum grid spacing depends on the average distance between grid points, and on the type of grid being used. The computer can accommodate a very large, but finite, number of grid cells.

After the chosen grid has been fit over the data points, the computer calculates a weighted average value for each point of intersection on the grid. This is done by searching the adjacent grid cells for neighboring data points. The values at these neighboring data points are weighted according to their distance from the grid point, and all of the weighted values are averaged to give an estimated value for the grid point. Where data is sparse, each grid point may be smoothed by an average of the neighboring grid point values.

The next step can be to contour the calculated grid point values ( Figure 2 ). This is done one grid cell at a time by fitting a polynomial of given order to the grid square.

Figure 2

The computer will draw profiles along any chosen line of section on the contoured gridded surface. Cross sections are formed by stacking two or more different profiles made along the same line of section.

Handling of discontinuities such as faults will vary from program to program. Often, if the surface to be gridded is offset by a fault, the location and orientation of the fault trace must be included in the data input. The computer then will not average data points, nor will it contour, across the fault. If the location of an existing fault is not indicated, the computer may smooth across the fault.

Gridded profiles are fairly accurate in areas of dense data control. However, the accuracy breaks down in areas of poor control. Where sparse data is relatively evenly spaced, one solution is to choose a large grid size which will smooth the data to reveal only regional structural trends. When data points are clustered, it may be necessary to smooth or even to omit the data in the intervening areas of poor coverage.

Several advantages are evident in the gridded profile method of cross section generation. First, a straight line of section can be chosen with or without regard to the location of wells. Second, any number of arbitrarily chosen profiles or cross sections can be made quickly over the same region. However, one must be careful to check the grid size and the extent of What are the benefits of a computerized cross section, and what are its limitations?

data control since these factors will affect the accuracy of the gridded profile.

In situations where large quantities of data must be sorted and arranged, a computer can frequently do the job faster than a person can. The preliminary aspects of constructing a section-organizing data, hanging logs and sticks on the datum line, and making initial correlations-are time consuming, and can be done quickly by a properly programmed computer. using a computer it is also possible to vary the parameters of a cross section until the most effective diagram is obtained.

However, the computer cannot make value judgements. Limitations arise because of the intuitive element in interpretation. For instance, the factors that suggest a fault or an unconformity to a geologist are often difficult to quantify-and they are even more difficult to incorporate into a computer program. There is still no substitute for human expertise.